re Digest 6186, Phi Scales

Rick: Use 11 (the octave complement of 25 in 36-tet) as it generates a mode (cyclic permutation) of same scale. The series of MOS are in successive intervals ascending are below:
11 25 (0 11 36)
11 11 14 (0 11 22 36)
11 11 11 3 ( 0 11 22 33 36)
8 3 8 3 8 3 3 The 7-tone MOS. (0 8 11 19 22 30 33 36)
5 3 3 5 3 3 5 3 3 3 The 10-tone MOS etc.
2 3 3 3 2 3 3 3 2 3 3 3 3 The 13-tone MOS
(2 2 1 2 1 2 1) (2 2 1 2 1 2 1) (2 2 1 2 1 2 1) 2 1 the 23-tone MOS.

--John

--- In tuning@yahoogroups.com, "John H. Chalmers" <JHCHALMERS@...> wrote:
>
> Rick: Use 11 (the octave complement of 25 in 36-tet) as it generates a
> mode (cyclic permutation) of same scale. The series of MOS are in
> successive intervals ascending are below:
> 11 25 (0 11 36)
> 11 11 14 (0 11 22 36)
> 11 11 11 3 ( 0 11 22 33 36)
> 8 3 8 3 8 3 3 The 7-tone MOS. (0 8 11 19 22 30 33 36)
> 5 3 3 5 3 3 5 3 3 3 The 10-tone MOS etc.
> 2 3 3 3 2 3 3 3 2 3 3 3 3 The 13-tone MOS
> (2 2 1 2 1 2 1) (2 2 1 2 1 2 1) (2 2 1 2 1 2 1) 2 1 the 23-tone MOS.
>
>
> --John
>
Thanks John, I was just about to post that (your message to me) myself for general consumption.

Btw, do you know if Young or somebody else did any work on the new symmetries that come out of a 36 EDO? Obviously there is successive apps of 5, perhaps up to 25. But there is also a 9 note scale/chord which comes from adding 4's. This is interesting because 8 gives an interval very close to 7/6, the flattened (harmonic) minor third, yet this scale also includes 12 and its compliment 24 which forms an augmented triad. So we have a type of "dim-aug" chord together. Knowing how both apply to standard harmony (eg Jazz), usually substituting the dominant chord, I thought this might give us a "way in" to include 25 in cycling etc...

PS: Aaron (AKA AKJ) also mentioned that PHI could give us key centres which are maximum distances apart, much like it is used in nature to separate the leaves of plants to gain maximum sunlight (forget the word, Phyllo-something). I have a vague idea that we could begin with the key at 25 and, using more or less standard chords, go through a long cycle back to 0 (similar to starting with Gb half-dim, the most distant key from C in 12 EDO, and cycling back to C maj).

-Rick

If you mean a Gb half dimished scale, then:

- it's not a key, it's only scale (enharmonically F#-G#-A-B-C-D-E, based on half diminished chord F#-A-C-E). But we can say it's relative to A minor key.

- it's not "the most distant" from C, as it is 6th mode of A melodic minor upwards, so notes A-B-C-D-E are as well in C major

Daniel Forro

On 15 May 2009, at 12:22 PM, rick_ballan wrote:

> (similar to starting with Gb half-dim, the most distant key from C > in 12 EDO, and cycling back to C maj).

--- In tuning@yahoogroups.com, Daniel Forro <dan.for@...> wrote:
>
> If you mean a Gb half dimished scale, then:
>
> - it's not a key, it's only scale (enharmonically F#-G#-A-B-C-D-E,
> based on half diminished chord F#-A-C-E). But we can say it's
> relative to A minor key.
>
> - it's not "the most distant" from C, as it is 6th mode of A melodic
> minor upwards, so notes A-B-C-D-E are as well in C major
>
> Daniel Forro
>
This is just jazz slang, Gb major most distant key from C becomes "C-ified" by making it half-dim and then cycling i.e. it is the furthest cycle from C.

-Rick
>
> On 15 May 2009, at 12:22 PM, rick_ballan wrote:
>
> > (similar to starting with Gb half-dim, the most distant key from C
> > in 12 EDO, and cycling back to C maj).
>